A linear function can be used to estimate the decrease in snowfall measured since 1920. The decrease in the annual snowfall has been on average 0.24 inches per year. Let x represent the number of years since 1920, when the measurements began, and let y represent the annual snowfall. The initial measurement in 1920 was 48.6 inches. Using the average change and initial measurement, which is the best estimate of the annual snowfall in the 78th year after records were kept? Round to the nearest hundredth.

29.88 inches

Step-by-step explanation:

Equation of a line is given in the form  

Where

m is the slope [rate of change, here, rate of decrease]

c is the y-intercept [at 1920, the snowfall]

From the problem, we see that snowfall decreases by 0.24 inches per year, that will make the slope (m) to be -0.24

Also, at 1920, the initial measurement was 48.6 inches of snow, that is the y-intercept (b). Thus, we can write the equation of this line as:

y = mx + b

y = -0.24 x +48.6

To find annual snowfall, 78th year after 1920, we simply plug in 78 into "x" of the equation just found. So:

y = -0.24(78) + 48.6 = 29.88 inches

answer:   x = 3 + √11     and     x = 3 - √11

step-by-step explanation:

x² - 6x + 9 = 11

(x - 3)² = 11

x - 3 = ±√11

    x = 3 ± √11

x = 3 + √11     and     x = 3 - √11